The World Bank records the prevalence of HIV in countries around the world. According to their data, “Prevalence of HIV refers to the percentage of people ages 15 to 49 who are infected with HIV.”[1] In South Africa, the prevalence of HIV is 17.3%. Let X = the number of people you test until you find a person infected with HIV.

a. Sketch a graph of the distribution of the discrete random variable X.

b. What is the probability that you must test 30 people to find one with HIV?

c. What is the probability that you must ask ten people?

d. Find the (i) mean and (ii) standard deviation of the distribution of X.